Type D solutions of 3D new massive gravity
Abstract
In a recent reformulation of threedimensional new massive gravity, the field equations of the theory consist of a massive (tensorial) KleinGordon type equation with a curvaturesquared source term and a constraint equation. Using this framework, we present all algebraic type D solutions of new massive gravity with constant and nonconstant scalar curvatures. For constant scalar curvature, they include homogeneous anisotropic solutions which encompass both solutions originating from topologically massive gravity, Bianchi types II, VIII, IX, and those of nontopologically massive gravity origin, Bianchi types VI{sub 0} and VII{sub 0}. For a special relation between the cosmological and mass parameters, {lambda}=m{sup 2}, they also include conformally flat solutions, and, in particular, those being locally isometric to the previouslyknown KaluzaKlein type AdS{sub 2}xS{sup 1} or dS{sub 2}xS{sup 1} solutions. For nonconstant scalar curvature, all the solutions are conformally flat and exist only for {lambda}=m{sup 2}. We find two general metrics which possess at least one Killing vector and comprise all such solutions. We also discuss some properties of these solutions, delineating among them black hole type solutions.
 Authors:

 Feza Guersey Institute, Cengelkoey, 34684 Istanbul (Turkey)
 Publication Date:
 OSTI Identifier:
 21541498
 Resource Type:
 Journal Article
 Journal Name:
 Physical Review. D, Particles Fields
 Additional Journal Information:
 Journal Volume: 83; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.83.084032; (c) 2011 American Institute of Physics; Journal ID: ISSN 05562821
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANISOTROPY; BLACK HOLES; GRAVITATION; KALUZAKLEIN THEORY; KLEINGORDON EQUATION; MASS; MATHEMATICAL SOLUTIONS; METRICS; THREEDIMENSIONAL CALCULATIONS; DIFFERENTIAL EQUATIONS; EQUATIONS; FIELD EQUATIONS; FIELD THEORIES; PARTIAL DIFFERENTIAL EQUATIONS; UNIFIEDFIELD THEORIES; WAVE EQUATIONS
Citation Formats
Ahmedov, Haji, and Aliev, Alikram N. Type D solutions of 3D new massive gravity. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVD.83.084032.
Ahmedov, Haji, & Aliev, Alikram N. Type D solutions of 3D new massive gravity. United States. https://doi.org/10.1103/PHYSREVD.83.084032
Ahmedov, Haji, and Aliev, Alikram N. Fri .
"Type D solutions of 3D new massive gravity". United States. https://doi.org/10.1103/PHYSREVD.83.084032.
@article{osti_21541498,
title = {Type D solutions of 3D new massive gravity},
author = {Ahmedov, Haji and Aliev, Alikram N},
abstractNote = {In a recent reformulation of threedimensional new massive gravity, the field equations of the theory consist of a massive (tensorial) KleinGordon type equation with a curvaturesquared source term and a constraint equation. Using this framework, we present all algebraic type D solutions of new massive gravity with constant and nonconstant scalar curvatures. For constant scalar curvature, they include homogeneous anisotropic solutions which encompass both solutions originating from topologically massive gravity, Bianchi types II, VIII, IX, and those of nontopologically massive gravity origin, Bianchi types VI{sub 0} and VII{sub 0}. For a special relation between the cosmological and mass parameters, {lambda}=m{sup 2}, they also include conformally flat solutions, and, in particular, those being locally isometric to the previouslyknown KaluzaKlein type AdS{sub 2}xS{sup 1} or dS{sub 2}xS{sup 1} solutions. For nonconstant scalar curvature, all the solutions are conformally flat and exist only for {lambda}=m{sup 2}. We find two general metrics which possess at least one Killing vector and comprise all such solutions. We also discuss some properties of these solutions, delineating among them black hole type solutions.},
doi = {10.1103/PHYSREVD.83.084032},
url = {https://www.osti.gov/biblio/21541498},
journal = {Physical Review. D, Particles Fields},
issn = {05562821},
number = 8,
volume = 83,
place = {United States},
year = {2011},
month = {4}
}